This project develops new statistical methods for epidemiology with broad applications and also methods as needed for ongoing projects in epidemiology, particularly those related to reproductive studies. The work this year involved several projects. (1) One project applied modern causal theory based on directed acyclic graphs to a classic scenario described by Weinberg and showed that the DAG approach leads to the same conclusions regarding appropriate adjustments that should be undertaken in an etiologic model; (2) Another project concerns pooled assessment of expensive-to-assay biomarkers based on human samples. Earlier work had shown that in a case-control setting one can pool together specimens from sets of cases and sets of controls and carry out a set-based analysis. With a slightly modified logistic model that analysis can estimate the individual-level risk parameters and loses almost no power compared to analysis based on individual assays. This means that if an exposure is based on an expensive assay that uses human samples, one can markedly improve efficiency by pooling specimens prior to assay. In recent work, we have extended these methods to apply to a fine-matched case-control design and also to time-to-pregnancy data. With the latter design, one pools specimens within strata defined by the time to conception. Again the power suffers almost not at all, compared to individual level assays, and the costs are greatly reduced. Another great benefit to pooling in general is in its conservative use of irreplaceable human specimens. For example, pooling specimens in sets of 3 reduces the amount needed from each specimen by 2/3. We have a paper that was published last year on use of pooling in a fine-matched case-control study, and another paper that is under revision for the American Journal of Epidemiology on using outcome-dependent pooling in the context of time-to-event data, e.g. time to pregnancy studies. Although these methods can produce huge cost savings and spare precious samples, the methods impose restrictions that limit the flexibility of models that can be fit. For example, one cannot explore secondary endpoints and one cannot fit nonlinear dose-logit-response models. We are now doing additional work aimed at developing semi-parametric methods for prospective pooling, which will overcome some of the limitations caused by the need to use outcome-dependent pooling. We are now developing semi-parametric methods for prospective pooling in time-to-event settings. Such methods should allow powerful and inexpensive assessments of the effects of environmental exposures on survival and other failure-time outcomes. (3) A third project is developing methods for analysis of outcomes related to environmental exposures where the exposure biomarker is often at a level below the assay limit of detection. Methods developed for survival analysis can be employed and permit confounder adjustment. We are applying this to data from the National Health and Nutrition Examination Survey data relating toxic analytes in blood to the presence of a biomarker, anti-nuclear antibodies, for autoimmunity.